求15个因式分解的题和答案 因式分解练习题及答案，求！！！
\u6c4220\u9053\u56e0\u5f0f\u5206\u89e3\u7684\u9898\u548c\u7b54\u6848 \u6025\u554a\u5feb\uff01\uff01\uff01\uff01\uff01 \u4e0d\u8981\u586b\u7a7a\u9009\u62e9\u7c7b\u76841.\u82e52x3\uff0b3x2\uff0bmx\uff0b1\u4e3ax\uff0b1\u7684\u500d\u5f0f,\u5219m\uff1d
2.\u56e0\u5f0f\u5206\u89e33a3b2c\uff0d6a2b2c2\uff0b9ab2c3\uff1d
3.\u56e0\u5f0f\u5206\u89e3xy\uff0b6\uff0d2x\uff0d3y\uff1d
4.\u56e0\u5f0f\u5206\u89e3x2(x\uff0dy)\uff0by2(y\uff0dx)\uff1d
5.\u56e0\u5f0f\u5206\u89e32x2\uff0d(a\uff0d2b)x\uff0dab\uff1d
6.\u56e0\u5f0f\u5206\u89e3a4\uff0d9a2b2\uff1d
7.\u82e5\u5df2\u77e5x3\uff0b3x2\uff0d4\u542b\u6709x\uff0d1\u7684\u56e0\u5f0f,\u8bd5\u5206\u89e3x3\uff0b3x2\uff0d4\uff1d
8.\u56e0\u5f0f\u5206\u89e3ab(x2\uff0dy2)\uff0bxy(a2\uff0db2)\uff1d
9.\u56e0\u5f0f\u5206\u89e3(x\uff0by)(a\uff0db\uff0dc)\uff0b(x\uff0dy)(b\uff0bc\uff0da)\uff1d
10.\u56e0\u5f0f\u5206\u89e3a2\uff0da\uff0db2\uff0db\uff1d
11.\u56e0\u5f0f\u5206\u89e3(3a\uff0db)2\uff0d4(3a\uff0db)(a\uff0b3b)\uff0b4(a\uff0b3b)2\uff1d
12.\u56e0\u5f0f\u5206\u89e3(a\uff0b3)2\uff0d6(a\uff0b3)\uff1d
13.\u56e0\u5f0f\u5206\u89e3(x\uff0b1)2(x\uff0b2)\uff0d(x\uff0b1)(x\uff0b2)2\uff1d
14.\u82e52\u00d74\u00d7(32\uff0b1)\u00d7(34\uff0b1)\u00d7(38\uff0b1)\u00d7(316\uff0b1)\uff1d3n\uff0d1,\u6c42n\uff1d .
15.\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f,\u6c42\u6807\u51c6\u5206\u89e3\u5f0f4891\uff1d .
16.2x\uff0b1\u662f\u4e0d\u662f4x2\uff0b5x\uff0d1\u7684\u56e0\u5f0f?\u7b54\uff1a.
17.\u82e56x2\uff0d7x\uff0bm\u662f2x\uff0d3\u7684\u500d\u5f0f,\u5219m\uff1d
18.x2\uff0b2x\uff0b1\u4e0ex2\uff0d1\u7684\u516c\u56e0\u5f0f\u4e3a .
19.\u82e5x\uff0b2\u662fx2\uff0bkx\uff0d8\u7684\u56e0\u5f0f,\u6c42k\uff1d .
20.\u82e54x2\uff0b8x\uff0b3\u662f2x\uff0b1\u7684\u500d\u5f0f\u8bf7\u56e0\u5f0f\u5206\u89e34x2\uff0b8x\uff0b3\uff1d .
21.2x\uff0b1\u662f4x2\uff0b8x\uff0b3\u7684\u56e0\u5f0f,\u8bf7\u56e0\u5f0f\u5206\u89e34x2\uff0b8x\uff0b3\uff1d .
22.(1)x\uff0b2 (2)x\uff0b4 (3)x\uff0b6 (4)x\uff0d6 (5)x2\uff0b2x3\uff0b24 \u4e0a\u5217\u4f55\u8005x2\uff0d2x\uff0d24\u7684\u56e0\u5f0f \uff08\u5168\u5bf9\u624d\u7ed9\u5206\uff09
23.\u56e0\u5f0f\u5206\u89e3\u4e0b\u5217\u5404\u5f0f\uff1a
(1)abc\uff0bab\uff0d4a\uff1d .
(2)16x2\uff0d81\uff1d .
(3)9x2\uff0d30x\uff0b25\uff1d .
(4)x2\uff0d7x\uff0d30\uff1d .
24.\u82e5x2\uff0bax\uff0d12\uff1d(x\uff0bb)(x\uff0d2),\u5176\u4e2da\u3001b\u5747\u4e3a\u6574\u6570,\u5219ab\uff1d .
25.\u8bf7\u5c06\u9002\u5f53\u7684\u6570\u586b\u5165\u7a7a\u683c\u4e2d\uff1ax2\uff0d16x\uff0b \uff1d(x\uff0d )2.
26.\u56e0\u5f0f\u5206\u89e3\u4e0b\u5217\u5404\u5f0f\uff1a
(1)xy\uff0dxz\uff0bx\uff1d \uff1b(2)6(x\uff0b1)\uff0dy(x\uff0b1)\uff1d
(3)x2\uff0d5x\uff0dpx\uff0b5p\uff1d \uff1b(4)15x2\uff0d11x\uff0d14\uff1d
27.\u8bbe7x2\uff0d19x\uff0d6\uff1d(7x\uff0ba)(bx\uff0d3),\u4e14a,b\u4e3a\u6574\u6570,\u52192a\uff0bb\uff1d
28.\u5229\u7528\u4e58\u6cd5\u516c\u5f0f\u5c55\u5f0099982\uff0d4\uff1d .
29.\u8ba1\u7b97(1.99)2\uff0d4\u00d71.99\uff0b4\u4e4b\u503c\u4e3a .
30.\u82e5x2\uff0bax\uff0d12\u53ef\u5206\u89e3\u4e3a(x\uff0b6)(x\uff0bb),\u4e14a,b\u4e3a\u6574\u6570,\u5219a\uff0bb\uff1d .
31.\u5df2\u77e59x2\uff0dmx\uff0b25\uff1d(3x\uff0dn)2,\u4e14n\u4e3a\u6b63\u6574\u6570,\u5219m\uff0bn\uff1d .
32.\u82e52x3\uff0b11x2\uff0b18x\uff0b9\uff1d(x\uff0b1)(ax\uff0b3)(x\uff0bb),\u5219a\uff0db\uff1d .
33.2992\uff0d3992\uff1d
34.\u586b\u5165\u9002\u5f53\u7684\u6570\u4f7f\u5176\u80fd\u6210\u4e3a\u5b8c\u5168\u5e73\u65b9\u5f0f4x2\uff0d20x\uff0b .
35.\u56e0\u5f0f\u5206\u89e3x2\uff0d25\uff1d .
36.\u56e0\u5f0f\u5206\u89e3x2\uff0d20x\uff0b100\uff1d .
37.\u56e0\u5f0f\u5206\u89e3x2\uff0b4x\uff0b3\uff1d .
38.\u56e0\u5f0f\u5206\u89e34x2\uff0d12x\uff0b5\uff1d .
39.\u56e0\u5f0f\u5206\u89e3\u4e0b\u5217\u5404\u5f0f\uff1a
(1)3ax2\uff0d6ax\uff1d .
(2)x(x\uff0b2)\uff0dx\uff1d .
(3)x2\uff0d4x\uff0dax\uff0b4a\uff1d .
(4)25x2\uff0d49\uff1d .
(5)36x2\uff0d60x\uff0b25\uff1d .
(6)4x2\uff0b12x\uff0b9\uff1d .
(7)x2\uff0d9x\uff0b18\uff1d .
(8)2x2\uff0d5x\uff0d3\uff1d .
(9)12x2\uff0d50x\uff0b8\uff1d .
40.\u56e0\u5f0f\u5206\u89e3(x\uff0b2)(x\uff0d3)\uff0b(x\uff0b2)(x\uff0b4)\uff1d .
41.\u56e0\u5f0f\u5206\u89e32ax2\uff0d3x\uff0b2ax\uff0d3\uff1d .
42.\u56e0\u5f0f\u5206\u89e39x2\uff0d66x\uff0b121\uff1d .
43.\u56e0\u5f0f\u5206\u89e38\uff0d2x2\uff1d .
44.\u56e0\u5f0f\u5206\u89e3x2\uff0dx\uff0b14 \uff1d .
45.\u56e0\u5f0f\u5206\u89e39x2\uff0d30x\uff0b25\uff1d .
46.\u56e0\u5f0f\u5206\u89e3\uff0d20x2\uff0b9x\uff0b20\uff1d .
47.\u56e0\u5f0f\u5206\u89e312x2\uff0d29x\uff0b15\uff1d .
48.\u56e0\u5f0f\u5206\u89e336x2\uff0b39x\uff0b9\uff1d .
49.\u56e0\u5f0f\u5206\u89e321x2\uff0d31x\uff0d22\uff1d .
50.\u56e0\u5f0f\u5206\u89e39x4\uff0d35x2\uff0d4\uff1d .
51.\u56e0\u5f0f\u5206\u89e3(2x\uff0b1)(x\uff0b1)\uff0b(2x\uff0b1)(x\uff0d3)\uff1d .
52.\u56e0\u5f0f\u5206\u89e32ax2\uff0d3x\uff0b2ax\uff0d3\uff1d .
53.\u56e0\u5f0f\u5206\u89e3x(y\uff0b2)\uff0dx\uff0dy\uff0d1\uff1d .
54.\u56e0\u5f0f\u5206\u89e3(x2\uff0d3x)\uff0b(x\uff0d3)2\uff1d .
55.\u56e0\u5f0f\u5206\u89e39x2\uff0d66x\uff0b121\uff1d .
56.\u56e0\u5f0f\u5206\u89e38\uff0d2x2\uff1d .
57.\u56e0\u5f0f\u5206\u89e3x4\uff0d1\uff1d .
58.\u56e0\u5f0f\u5206\u89e3x2\uff0b4x\uff0dxy\uff0d2y\uff0b4\uff1d .
59.\u56e0\u5f0f\u5206\u89e34x2\uff0d12x\uff0b5\uff1d .
60.\u56e0\u5f0f\u5206\u89e321x2\uff0d31x\uff0d22\uff1d .
61.\u56e0\u5f0f\u5206\u89e34x2\uff0b4xy\uff0by2\uff0d4x\uff0d2y\uff0d3\uff1d .
62.\u56e0\u5f0f\u5206\u89e39x5\uff0d35x3\uff0d4x\uff1d .
63.\u56e0\u5f0f\u5206\u89e3\u4e0b\u5217\u5404\u5f0f\uff1a
(1)3x2\uff0d6x\uff1d .
(2)49x2\uff0d25\uff1d .
(3)6x2\uff0d13x\uff0b5\uff1d .
(4)x2\uff0b2\uff0d3x\uff1d .
(5)12x2\uff0d23x\uff0d24\uff1d
140\uff0em2(p-q)-p+q
141\uff0e(2m+3n)(2m-n)-4n(2m-n)\uff0e
142\uff0e(x+2y)2-x2-2xy\uff0e
143\uff0ea(ab+bc+ac)-abc\uff0e
144\uff0eab-a-b+1\uff0e
145\uff0exyz-xy-xz+x-yz+y+z-1\uff0e
146\uff0ex4-2y4-2x3y+xy3\uff0e
148\uff0eabc(a2+b2+c2)-a3bc+2ab2c2\uff0e
149\uff0e(a-b-c)(a+b-c)-(b-c-a)(b+c-a)\uff0e
150\uff0ea2(b-c)+b2(c-a)+c2(a-b)\uff0e
a(a+b)(a-b)-a(a+b)2\uff0e
152\uff0e(x2-2x)2+2x(x-2)+1\uff0e
153\uff0e2acd-c2a-ad2\uff0e
154\uff0e(x-y)2+12(y-x)z+36z2\uff0e
156\uff0ex2-4ax+8ab-4b2\uff0e
157\uff0ea2b2+c2d2-2abcd+2ab-2cd+1\uff0e
158\uff0e(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx)\uff0e
160\uff0e(1-a2)(1-b2)-(a2-1)2(b2-1)2\uff0e
161\uff0e3x4-48y4\uff0e
162\uff0e(x+1)2-9(x-1)2\uff0e
163\uff0e(x2+pq)2-(p+q)2x2\uff0e
164\uff0e(1+2xy)2-(x2+y2)2\uff0e
165\uff0e4a2b2-(a2+b2)2\uff0e
166\uff0e4a2b2-(a2+b2-c2)2\uff0e
167\uff0e(c2-a2-b2)2-4a2b2\uff0e
168\uff0e(x2-b2+y2-a2)2-4(ab-xy)2\uff0e
169\uff0e64a4(x+1)2-49b4(x+1)4\uff0e
170\uff0eab2-ac2+4ac-4a\uff0e
171\uff0e4a2-c2+6ab+3bc\uff0e
172\uff0ex3n+y3n\uff0e
174\uff0e(x+y)3+125\uff0e
176\uff0e(m-n)6-(m+n)6\uff0e
177\uff0e(x+1)6-(x-1)6\uff0e
178\uff0ea12-b12\uff0e
179\uff0e(z-x)3-(y+z)3\uff0e
180\uff0e(3m-2n)3+(3m+2n)3\uff0e
181\uff0ex6(x2-y2)+y6(y2-x2)\uff0e
182\uff0e8(x+y)3+1\uff0e
183\uff0e(a-1)3-(b+1)3\uff0e
184\uff0e(a+b+c)3-a3-b3-c3\uff0e
185\uff0ex2+4xy+3y2\uff0e
186\uff0ex2y2-18xy+65\uff0e
187\uff0ex2+18x-144\uff0e
188\uff0ex2+30x+144\uff0e
189\uff0ex4+2x2-8\uff0e
190\uff0e3x4+6x2-9\uff0e
191\uff0e-m4+18m2-17\uff0e
192\uff0e3x4-7x2y2-20y4\uff0e
193\uff0ex5-2x3-8x\uff0e
194\uff0ea3-5a2b-300ab2\uff0e
195\uff0ex8+19x5-216x2\uff0e
196\uff0e6a4n+k-a2n+k-35ak\uff0e
199\uff0e30x2+8xy-182y2\uff0e
200\uff0em4+14m2-15\uff0e
140\uff0e\uff08p-q\uff09\uff08m-1\uff09\uff08m+1\uff09\uff0e
141\uff0e\uff082m-n\uff092\uff0e
142\uff0e2y\uff08x+2y\uff09\uff0e
143\uff0ea2\uff08b+c\uff09\uff0e
144\uff0e\uff08b-1\uff09\uff08a-1\uff09\uff0e
145\uff0e\uff08x-1\uff09\uff08y-1\uff09\uff08z-1\uff09\uff0e
\u63d0\u793a\uff1a\u65b9\u6cd5\u4e00 \u539f\u5f0f=x\uff08yz-y-z+1\uff09-\uff08yz-y-z+1\uff09
=\uff08yz-y-z+1\uff09\uff08x-1\uff09
=[y\uff08z-1\uff09-\uff08z-1\uff09]\uff08x-1\uff09
=\uff08x-1\uff09\uff08y-1\uff09\uff08z-1\uff09\uff0e
\u65b9\u6cd5\u4e8c \u539f\u5f0f=xy\uff08z-1\uff09-x\uff08z-1\uff09-y\uff08z-1\uff09+\uff08z-1\uff09
=\uff08xy-x-y+1\uff09\uff08z-1\uff09
=[x\uff08y-1\uff09-\uff08y-1\uff09]\uff08z-1\uff09
=\uff08x-1\uff09\uff08y-1\uff09\uff08z-1\uff09\uff0e
146\uff0e\uff08x-2y\uff09\uff08x+y\uff09\uff08x2-xy+y2\uff09\uff0e
\u63d0\u793a\uff1a\u65b9\u6cd5\u4e00 \u539f\u5f0f=x\uff08x3+y3\uff09-2y\uff08x3+y3\uff09
=\uff08x3+y3\uff09\uff08x-2y\uff09
=\uff08x-2y\uff09\uff08x+y\uff09\uff08x2-xy+y2\uff09\uff0e
\u65b9\u6cd5\u4e8c \u539f\u5f0f=x3\uff08x-2y\uff09+y3\uff08x-2y\uff09
=\uff08x-2y\uff09\uff08x3+y3\uff09
=\uff08x-2y\uff09\uff08x+y\uff09\uff08x2-xy+y2\uff09\uff0e
148\uff0eabc\uff08b+c\uff092\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=abc\uff08a2+b2+c2-a2+2bc\uff09\uff0e
149\uff0e2\uff08b-c\uff09\uff08a-b-c\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff08a-b-c\uff09\uff08a+b-c\uff09+\uff08a-b-c\uff09\uff08b-c-a\uff09
=\uff08a-b-c\uff09[\uff08a+b-c\uff09+\uff08b-c-a\uff09]
=2\uff08b-c\uff09\uff08a-b-c\uff09\uff0e
150\uff0e\uff08a-b\uff09\uff08b-c\uff09\uff08a-c\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=a2b-a2c+b2c-ab2+c2\uff08a-b\uff09
=\uff08a2b-ab2\uff09-\uff08a2c-b2c\uff09+c2\uff08a-b\uff09
=ab\uff08a-b\uff09-c\uff08a2-b2\uff09+c2\uff08a-b\uff09
=\uff08a-b\uff09[ab-c\uff08a+b\uff09+c2]
=\uff08a-b\uff09[a\uff08b-c\uff09-c\uff08b-c\uff09]
=\uff08a-b\uff09\uff08b-c\uff09\uff08a-c\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=a\uff08a+b\uff09[a-b-\uff08a+b\uff09]=a\uff08a+b\uff09\uff08-2b\uff09
=-2ab\uff08a+b\uff09\uff1b
152\uff0e\uff08x-1\uff094\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=[x\uff08x-2\uff09]2+2•x\uff08x-2\uff09+12
=[x\uff08x-2\uff09+1]2=\uff08x2-2x+1\uff092
=\uff08x-1\uff094\uff0e
153\uff0e-a\uff08c-d\uff092\uff0e
154\uff0e\uff08x-y-6z\uff092\uff0e
156\uff0e\uff08x-2b\uff09\uff08x-4a+2b\uff09\uff0e
157\uff0e\uff08ab-cd+1\uff092\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff08a2b2-2abcd+c2d2\uff09+2\uff08ab-cd\uff09+1
=\uff08ab-cd\uff092+2\uff08ab-cd\uff09+1
=\uff08ab-cd+1\uff092\uff0e
158\uff0e\uff08ax+by+ay-bx\uff092\uff0e
160\uff0e\uff081+a\uff09\uff081-a\uff09\uff081+b\uff09\uff081-b\uff09\uff08a2+b2-a2b2\uff09\uff0e
161\uff0e3\uff08x2+4y2\uff09\uff08x+2y\uff09\uff08x-2y\uff09\uff0e
162\uff0e4\uff082x-1\uff09\uff082-x\uff09\uff0e
163\uff0e\uff08x2+px+qx+pq\uff09\uff08x2-px-qx+pq\uff09\uff0e
164\uff0e\uff081+x-y\uff09\uff081-x+y\uff09\uff08x2+y2+2xy+1\uff09\uff0e
165\uff0e-\uff08a+b\uff092\uff08a-b\uff092\uff0e
166\uff0e\uff08a+b+c\uff09\uff08a+b-c\uff09\uff08c+a-b\uff09\uff08c-a+b\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff082ab+a2+b2-c2\uff09\uff082ab-a2-b2+c2\uff09
=[\uff08a+b\uff092-c2][c2-\uff08a-b\uff092]
=\uff08a+b+c\uff09\uff08a+b-c\uff09\uff08c+a-b\uff09\uff08c-a+b\uff09\uff0e
167\uff0e\uff08c+a-b\uff09\uff08c-a+b\uff09\uff08c+a+b\uff09\uff08c-a-b\uff09\uff0e
168\uff0e\uff08x+y+a+b\uff09\uff08x+y-a-b\uff09\uff08x-y+a-b\uff09\uff08x-y-a+b\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff08x2-b2+y2-a2+2ab-2xy\uff09\uff08x2-b2+y2-a2-2ab+2xy\uff09
=[\uff08x2-2xy+y2\uff09-\uff08a2-2ab+b2\uff09][\uff08x2+2xy+y2\uff09
-\uff08a2+2ab+b2\uff09]
=[\uff08x-y\uff092-\uff08a-b\uff092][\uff08x+y\uff092-\uff08a+b\uff092]
=\uff08x-y+a-b\uff09\uff08x-y-a+b\uff09\uff08x+y+a+b\uff09\uff08x+y-a-b\uff09\uff0e
169\uff0e\uff08x+1\uff092\uff088a2+7b2x+7b2\uff09\uff088a2-7b2x-7b2\uff09\uff0e
170\uff0ea\uff08b-c+2\uff09\uff08b+c-2\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=a\uff08b2-c2+4c-4\uff09
=a\uff08b2-c2+2b-2b+2c+2c-4\uff09
=a[\uff08b-c\uff09\uff08b+c\uff09-2\uff08b-c\uff09+2\uff08b+c\uff09-4]
=a[\uff08b-c\uff09+2][\uff08b+c\uff09-2]\uff0e
171\uff0e\uff082a+c\uff09\uff082a-c+3b\uff09\uff0e
172\uff0e\uff08xn+yn\uff09\uff08x2n-xnyn+y2n\uff09\uff0e
174\uff0e\uff08x+y+5\uff09\uff08x2+2xy+y2-5x-5y+25\uff09\uff0e
176\uff0e-4mn\uff083n2+m2\uff09\uff083m2+n2\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=[\uff08m-n\uff093]2-[\uff08m+n\uff093]2
=[\uff08m-n\uff093+\uff08m+n\uff093][\uff08m-n\uff093-\uff08m+n\uff093]
=2m[\uff08m-n\uff092-\uff08m-n\uff09\uff08m+n\uff09\uff08m+n\uff092]
\u00d7{-2n[\uff08m-n\uff092+\uff08m-n\uff09\uff08m+n\uff09+\uff08m+n\uff092]}
=-4mn\uff08m2+3n2\uff09\uff083m2+n2\uff09\uff0e
177\uff0e4x\uff08x2+3\uff09\uff083x2+1\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=[\uff08x+1\uff093]2-[\uff08x-1\uff093]2
=[\uff08x+1\uff093+\uff08x-1\uff093][\uff08x+1\uff093-\uff08x-1\uff093]
=2x[\uff08x+1\uff092-\uff08x+1\uff09\uff08x-1\uff09+\uff08x-1\uff092]
\u00d72[\uff08x+1\uff092+\uff08x+1\uff09\uff08x-1\uff09+\uff08x-1\uff092]
=4x\uff08x2+3\uff09\uff083x2+1\uff09\uff0e
178\uff0e\uff08a-b\uff09\uff08a+b\uff09\uff08a2+b2\uff09\uff08a2+ab+b2\uff09\uff08a2-ab+b2\uff09\uff08a4-a2b2+b4\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff08a6\uff092-\uff08b6\uff092=\uff08a6+b6\uff09\uff08a6-b6\uff09
=[\uff08a2\uff093+\uff08b2\uff093][\uff08a3\uff092-\uff08b3\uff092]
=\uff08a2+b2\uff09\uff08a4-a2b2+b4\uff09\uff08a3+b3\uff09\uff08a3-b3\uff09\uff0e
179\uff0e-\uff08x+y\uff09\uff08x2+y2+3z2-xy+3yz-3xz\uff09\uff0e
180\uff0e18m\uff083m2+4n2\uff09\uff0e
181\uff0e\uff08x+y\uff092\uff08x-y\uff092\uff08x2-xy+y2\uff09\uff08x2+xy+y2\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=\uff08x2-y2\uff09\uff08x6-y6\uff09
=\uff08x+y\uff09\uff08x-y\uff09\uff08x3+y3\uff09\uff08x3-y3\uff09\uff0e
182\uff0e\uff082x+2y+1\uff09\uff084x2+8xy+4y2-2x-2y+1\uff09\uff0e
183\uff0e\uff08a-b-2\uff09\uff08a2+ab+b2-a+b+1\uff09\uff0e
184\uff0e3\uff08b+c\uff09\uff08a+b\uff09\uff08c+a\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=[\uff08a+b+c\uff093-a3]-\uff08b3+c3\uff09\uff0e
185\uff0e\uff08x+3y\uff09\uff08x+y\uff09\uff0e
186\uff0e\uff08xy-13\uff09\uff08xy-5\uff09\uff0e
187\uff0e\uff08x-6\uff09\uff08x+24\uff09\uff0e
188\uff0e\uff08x+6\uff09\uff08x+24\uff09\uff0e
189\uff0e\uff08x2-2\uff09\uff08x2+4\uff09\uff0e
190\uff0e3\uff08x2+3\uff09\uff08x+1\uff09\uff08x-1\uff09\uff0e
191\uff0e\uff08m2-17\uff09\uff081+m\uff09\uff081-m\uff09\uff0e
192\uff0e\uff083x2+5y2\uff09\uff08x+2y\uff09\uff08x-2y\uff09\uff0e
193\uff0ex\uff08x+2\uff09\uff08x-2\uff09\uff08x2+2\uff09\uff0e
194\uff0ea\uff08a-20b\uff09\uff08a+15b\uff09\uff0e
195\uff0ex2\uff08x+3\uff09\uff08x2-3x+9\uff09\uff08x-2\uff09\uff08x2+2x+4\uff09\uff0e
\u63d0\u793a\uff1a\u539f\u5f0f=x2\uff08x6+19x3-216\uff09
=x2\uff08x3+27\uff09\uff08x3-8\uff09
=x3\uff08x+3\uff09\uff08x2-3x+9\uff09\uff08x-2\uff09\uff08x2+2x+4\uff09\uff0e
196\uff0eak\uff082a2n-5\uff09\uff083a2n+7\uff09\uff0e
199\uff0e2\uff083x-7y\uff09\uff085x+13y\uff09\uff0e
200\uff0e\uff08m2+15\uff09\uff08m+1\uff09\uff08m-1\uff09\uff0e
201\uff0em2(p\uff0dq)\uff0dp\uff0bq\uff1b
202\uff0ea(ab\uff0bbc\uff0bac)\uff0dabc\uff1b
203\uff0ex4\uff0d2y4\uff0d2x3y\uff0bxy3\uff1b
204\uff0eabc(a2\uff0bb2\uff0bc2)\uff0da3bc\uff0b2ab2c2\uff1b
205\uff0ea2(b\uff0dc)\uff0bb2(c\uff0da)\uff0bc2(a\uff0db)\uff1b
206\uff0e(x2\uff0d2x)2\uff0b2x(x\uff0d2)\uff0b1\uff1b
207\uff0e(x\uff0dy)2\uff0b12(y\uff0dx)z\uff0b36z2\uff1b
208\uff0ex2\uff0d4ax\uff0b8ab\uff0d4b2\uff1b
209\uff0e(ax\uff0bby)2\uff0b(ay\uff0dbx)2\uff0b2(ax\uff0bby)(ay\uff0dbx)\uff1b
210\uff0e(1\uff0da2)(1\uff0db2)\uff0d(a2\uff0d1)2(b2\uff0d1)2\uff1b
211\uff0e(x\uff0b1)2\uff0d9(x\uff0d1)2\uff1b
212\uff0e4a2b2\uff0d(a2\uff0bb2\uff0dc2)2\uff1b
213\uff0eab2\uff0dac2\uff0b4ac\uff0d4a\uff1b
214\uff0ex3n\uff0by3n\uff1b
215\uff0e(x\uff0by)3\uff0b125\uff1b
216\uff0e(3m\uff0d2n)3\uff0b(3m\uff0b2n)3\uff1b
217\uff0ex6(x2\uff0dy2)\uff0by6(y2\uff0dx2)\uff1b
218\uff0e8(x\uff0by)3\uff0b1\uff1b
219\uff0e(a\uff0bb\uff0bc)3\uff0da3\uff0db3\uff0dc3\uff1b
220\uff0ex2\uff0b4xy\uff0b3y2\uff1b
221\uff0ex2\uff0b18x\uff0d144\uff1b
222\uff0ex4\uff0b2x2\uff0d8\uff1b
223\uff0e\uff0dm4\uff0b18m2\uff0d17\uff1b
224\uff0ex5\uff0d2x3\uff0d8x\uff1b
225\uff0ex8\uff0b19x5\uff0d216x2\uff1b
226\uff0e(x2\uff0d7x)2\uff0b10(x2\uff0d7x)\uff0d24\uff1b
227\uff0e5\uff0b7(a\uff0b1)\uff0d6(a\uff0b1)2\uff1b
228\uff0e(x2\uff0bx)(x2\uff0bx\uff0d1)\uff0d2\uff1b
229\uff0ex2\uff0by2\uff0dx2y2\uff0d4xy\uff0d1\uff1b
230\uff0e(x\uff0d1)(x\uff0d2)(x\uff0d3)(x\uff0d4)\uff0d48\uff1b
231\uff0ex2\uff0dy2\uff0dx\uff0dy\uff1b
232\uff0eax2\uff0dbx2\uff0dbx\uff0bax\uff0d3a\uff0b3b\uff1b
233\uff0em4\uff0bm2\uff0b1\uff1b
234\uff0ea2\uff0db2\uff0b2ac\uff0bc2\uff1b
235\uff0ea3\uff0dab2\uff0ba\uff0db\uff1b
236\uff0e625b4\uff0d(a\uff0db)4\uff1b
237\uff0ex6\uff0dy6\uff0b3x2y4\uff0d3x4y2\uff1b
238\uff0ex2\uff0b4xy\uff0b4y2\uff0d2x\uff0d4y\uff0d35\uff1b
239\uff0em2\uff0da2\uff0b4ab\uff0d4b2\uff1b
240\uff0e5m\uff0d5n\uff0dm2\uff0b2mn\uff0dn2\uff0e
\u53c2\u8003\u7b54\u6848:
\u4e09\u3001\u56e0\u5f0f\u5206\u89e3\uff1a
1\uff0e(p\uff0dq)(m\uff0d1)(m\uff0b1)\uff0e
8\uff0e(x\uff0d2b)(x\uff0d4a\uff0b2b)\uff0e
11\uff0e4(2x\uff0d1)(2\uff0dx)\uff0e
20\uff0e(x\uff0b3y)(x\uff0by)\uff0e
21\uff0e(x\uff0d6)(x\uff0b24)\uff0e
27\uff0e(3\uff0b2a)(2\uff0d3a)\uff0e
31\uff0e(x\uff0by)(x\uff0dy\uff0d1)\uff0e
38\uff0e(x\uff0b2y\uff0d7)(x\uff0b2y\uff0b5)\uff0e
解原式=（x^15+m^12）+(m^9+m^6)+(m^3+1)
=m^12(m^3+1)+m^6(m^3+1)+(m^3+1)
=(m^3+1)(m^12+m^6++1)
=(m^3+1)[(m^6+1)2-m^6]
=(m^+1)(m^2-m^+1)(m^6+1+m^3)(m^6+1-m^3)
例2分解因式：x^4+5x^3+15x-9
解析可根据系数特征进行分组
解原式=（x^4-9）+5x^3+15x
=(x^2+3)(x2-3)+5x(x^2+3)
=(x^2+3)(x^2+5x-3)
1．下列因式分解中，正确的是（ ）���������
(A) 1- 14 x2= 14 (x + 2) (x- 2) (B)4x –2 x2 – 2 = - 2(x- 1)2
(C) ( x- y )3 –(y- x) = (x – y) (x – y + 1) ( x –y – 1)
(D) x2 –y2 – x + y = ( x + y) (x – y – 1)
2．下列各等式(1) a2－ b2 = (a + b) (a–b ),(2) x2–3x +2 = x(x–3) + 2
(3 ) 1 x2 –y2 －1 ( x + y) (x – y ) ,(4 )x2 + 1 x2 －2－（ x －1x )2
从左到是因式分解的个数为（ ）
(A) 1 个 (B) 2 个 (C) 3 个 (D) 4个
3．若x2＋mx＋25 是一个完全平方式，则m的值是（ ）
(A) 20 (B) 10 (C) ± 20 (D) ±10
4．若x2＋mx＋n能分解成( x+2 ) (x – 5)，则m= ,n= ;
5．若二次三项式2x2+x+5m在实数范围内能因式分解，则m= ;
6．若x2+kx－6有一个因式是(x－2)，则k的值是 ;
7．把下列因式因式分解：
(1)a3－a2－2a (2)4m2－9n2－4m+1
(3)3a2+bc－3ac-ab (4)9－x2+2xy－y2
8．在实数范围内因式分解：
(1)2x2－3x－1 (2)－2x2+5xy+2y2
考点训练：
1. 分解下列因式：
(1).10a(x－y)2－5b(y－x) (2).an+1－4an＋4an-1
(3).x3(2x－y)－2x＋y (4).x(6x－1)－1
(5).2ax－10ay＋5by＋6x (6).1－a2－ab－14 b2
*(7).a4＋4 (8).(x2＋x)(x2＋x－3)＋2
(9).x5y－9xy5 (10).－4x2＋3xy＋2y2
(11).4a－a5 (12).2x2－4x＋1
(13).4y2＋4y－5 (14)3X2－7X+2
解题指导：
1．下列运算:(1) (a－3)2＝a2－6a＋9 (2) x－4＝(x ＋2)( x －2)
(3) ax2＋a2xy＋a＝a(x2＋ax) (4) 116 x2－14 x＋14 ＝x2－4x＋4＝(x－2)2其中是因式分解，且运算正确的个数是（ ）
（A）1 （B）2 （C）3 （D）4
2．不论a为何值，代数式－a2＋4a－5值（ ）
（A）大于或等于0 （B）0 （C）大于0 （D）小于0
3．若x2＋2（m－3）x＋16 是一个完全平方式，则m的值是（ ）
（A）－5 （B）7 （C）－1 （D）7或－1
4．(x2＋y2)(x2－1＋y2)－12＝0,则x2＋y2的值是 ；
5．分解下列因式：
(1).8xy(x－y)－2(y－x)3 ＊(2).x6－y6
(3).x3＋2xy－x－xy2 ＊(4).(x＋y)(x＋y－1)－12
(5).4ab－（1－a2）（1－b2） (6).－3m2－2m＋4
＊4。已知a＋b＝1,求a3＋3ab＋b3的值
5．a、b、c为⊿ABC三边，利用因式分解说明b2－a2＋2ac－c2的符号
6．0＜a≤5，a为整数，若2x2＋3x＋a能用十字相乘法分解因式，求符合条件的a
独立训练：
1．多项式x2－y2, x2－2xy＋y2, x3－y3的公因式是 。
2．填上适当的数或式，使左边可分解为右边的结果：
(1)9x2－( )2＝(3x＋ )( －15 y), (2).5x2＋6xy－8y2＝(x )( －4y).
3．矩形的面积为6x2＋13x＋5 (x>0),其中一边长为2x＋1,则另为 。
4．把a2－a－6分解因式，正确的是( )
(A)a(a－1)－6 (B)(a－2)(a＋3) (C)(a＋2)(a－3) (D)(a－1)(a＋6)
5．多项式a2＋4ab＋2b2,a2－4ab＋16b2,a2＋a＋14 ,9a2－12ab＋4b2中，能用完全平方公式分解因式的有( )
(A) 1个 (B) 2个 (C) 3个 (D) 4个
6．设(x＋y)(x＋2＋y)－15＝0,则x＋y的值是（ ）
(A)-5或3 (B) -3或5 (C)3 (D)5
7．关于的二次三项式x2－4x＋c能分解成两个整系数的一次的积式，那么c可取下面四个值中的（ ）
(A) －8 (B) －7 (C) －6 (D) －5
8．若x2－mx＋n＝(x－4)(x＋3) 则m,n的值为（ ）
(A) m＝－1, n＝－12 (B)m＝－1,n＝12 (C) m＝1,n＝－12 (D) m＝1,n＝12.
9．代数式y2＋my＋254 是一个完全平方式，则m的值是 。
10．已知2x2－3xy＋y2＝0（x,y均不为零），则 xy ＋ yx 的值为 。
11．分解因式:
(1).x2(y－z)＋81(z－y) (2).9m2－6m＋2n－n2
＊(3).ab(c2＋d2)＋cd(a2＋b2) (4).a4－3a2－4
＊(5).x4＋4y4 ＊(6).a2＋2ab＋b2－2a－2b＋1
12．实数范围内因式分解
（1）x2－2x－4 （2）4x2＋8x－1 （3）2x2＋4xy＋y2
初二数学因式分解测试题
刘锦珍
一、 选择题：
1. 多项式15x3y4m2－35x4y2m2+20x3ym的各项公因式是（ ）
A 5x3y B 5x3ym C 5x3m D5x3m2y
2. 下列从左到右的变形中是因式分解的是（ ）
A (a+b)2=a2+2ab+b2 B x2-4x+5=(x-2x)2+1
C x2-5x-6=(x+6)(x-1) D x2-10x+25=(x-5)2
3. 若多项式x2+kxy+9y2是一个完全平方式，则k的值为（ ）
A 6 B 3 C －6 D －6或6
4. 把多项式a2+a-b2-b用分组分解法分解因式不同的分组方法有（ ）
A 1种 B 2种 C 3种 D 4种
5. 多项式a2+b2, x2-y2, -x2-y2, -a2+b2中，能分解因式的有（ ）
A 4个 B 3个 C 2个 D 1个
6. 如果多项式x2－mx－15能分解因式，则m的值为（ ）
A 2或－2 B 14或－14 C 2或－14 D ±2或±14
7. 下列各多项式中不含有因式 (x-1) 的是（ ）
A x3-x2-x+1 B x2+y-xy-x C x2-2x-y2+1 D (x2+3x)2-(2x+2)2
8. 若 则x为（ ）
A 1 B －1 C D －2
9. 若多项式4ab－4a2－b2－m有一个因式为（1-2a+b）则m的值为（ ）
A 0 B 1 C －1 D 4
10. 如果 (a2＋b2－3) (a2+b2) －10 = 0那么a2+b2的值为（ ）
A －2 B 5 C 2 D －2或5
二、分解下列各式：
1、- m2 – n2 + 2mn + 1 2、(a + b)3d – 4(a + b)2cd+4(a + b)c2d
3. (x + a)2 – (x – a)2 4.
5. –x5y – xy +2x3y 6. x6 – x4 – x2 + 1
7. (x +3) (x +2) +x2 – 9 8. (x –y)3 +9(x – y) –6(x – y)2
9. (a2 + b2 –1 )2 – 4a2b2 10. (ax + by)2 + (bx – ay)2
三、 简便方法计算：
1. 2.
四、 化简求值：
1. 2ax2 – 8axy + 8ay2 – 2a 2. 已知：a2 – b2 – 5=0 c2 – d2 – 2 =0
其中x –2 y =1 a=3 求：(ac + bd)2 – (ad + bc)2的值
五、 观察下列分解因式的过程： 分解因式的方法，叫做 配方法。
x2 + 2ax – 3a2 请你用配方法分解因式：
=x2+2ax+a2 – a2 – 3a2 （先加上a2,再减去a2） m2 – 4mn +3n2
=(x+a)2 – 4a2 （运用完全平方公式）
=(x+a+2a) (x+a – 2a) （运用平方差公式）
=(x+3a) (x – a)
像上面这样通过加减项配出完全平方式把二次三项式
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绛旓細1.ab³-4ab=ab(b²-4)=ab(b+2)(b-2)2.3x²y+12xy²+12y³=3y(x²+4xy+4y²)=3y(x+2y)²3.x³y-2x²y²+xy³=xy(x²-2xy+y²)=xy(x-y)²4.12a⁴b²-27a²b⁴...
绛旓細xy锛6锛2x锛3y锛(x-3)(y-2)4.鍥犲紡鍒嗚Вx2(x锛峺)锛媦2(y锛峹)锛(x+y)(x-y)^2 5.鍥犲紡鍒嗚В2x2锛(a锛2b)x锛峚b锛(2x-a)(x+b)6.鍥犲紡鍒嗚Вa4锛9a2b2锛漚^2(a+3b)(a-3b)7.鑻ュ凡鐭3锛3x2锛4鍚湁x锛1鐨勫洜寮忥紝璇曞垎瑙3锛3x2锛4锛(x-1)(x+2)^2 8.鍥犲紡鍒嗚Вab(x2锛峺2)...
绛旓細1.鍥犲紡鍒嗚В3a^3b^2c锛6a^2b^2c^2锛9ab^2c^3锛3ab^2 c(a^2-2ac+3c^2)2.鍥犲紡鍒嗚Вxy锛6锛2x锛3y锛(x-3)(y-2)3.鍥犲紡鍒嗚Вx^2(x锛峺)锛媦^2(y锛峹)锛(x+y)(x-y)^2 4.鍥犲紡鍒嗚В2x^2锛(a锛2b)x锛峚b锛(2x-a)(x+b)5.鍥犲紡鍒嗚Вa^4锛9a^2b^2锛漚^2(a+3b)(a-3b)...
绛旓細25.x2锛峹锛14 锛濇暣鏁板唴鏃犳硶鍒嗚В 26.9x2锛30x锛25锛(3x-5)^2 27.锛20x2锛9x锛20锛(-4x+5)(5x+4)28.12x2锛29x锛15锛(4x-3)(3x-5)29.36x2锛39x锛9锛3(3x+1)(4x+3)30.21x2锛31x锛22锛(21x+11)(x-2)31.9x4锛35x2锛4锛(9x^2+1)(x+2)(x-2)32.(2x锛1)(x...
绛旓細1銆=a^4+b^4+2a²b²-4a²b²=a^4+b^4-2a²b²=(a²-b²)²2銆=(a^4-b^4)(x-y)=(a+b)(a-b)(a²+b²)(x-y)3銆=(a²+1)²-2脳2a脳锛坅²+1锛+锛2a锛²=锛坅²-2a+1锛&...
绛旓細15銆3Y^-9Y+6=(3Y-6)(Y-1)16銆7X^2-10X+3=(7X-3)(X-1)17銆3X^2+5X+2=(3X+2)(X+1)18銆4X^+12X+9=(2X+3)(2X+3)19銆5Y^2-7Y-6=(5Y+3)(Y-2)20銆2Y^2-Y-6=(2Y+3)(Y-2)21銆2X^2-XY-Y^2=(2X+Y)(X-Y)22銆6X^2-2XY-4Y^2=(3X+2Y)(2X-2Y)23銆5X...
绛旓細42.鍥犲紡鍒嗚В9x2-66x+121= 銆43.鍥犲紡鍒嗚В8-2x2= 銆44.鍥犲紡鍒嗚Вx2-x+14 = 銆45.鍥犲紡鍒嗚В9x2-30x+25= 銆46.鍥犲紡鍒嗚В-20x2+9x+20= 銆47.鍥犲紡鍒嗚В12x2-29x+15= 銆48.鍥犲紡鍒嗚В36x2+39x+9= 銆49.鍥犲紡鍒嗚В21x2-31x-22= 銆50.鍥犲紡鍒嗚В9x4-35x2-4= 銆51.鍥犲紡鍒嗚В(2x+1)(x+...
绛旓細瑙ｏ細锛14锛夊師寮忥紳锛坅+b锛(a-b)(15)鍘熷紡锛(a+b)²锛16锛夊師寮忥紳x(x²-y)锛17锛夊師寮忥紳(x-y)²锛18锛夊師寮忥紳x(x-4)锛19锛夊師寮忥紳2(a²-4)锛2(a+2)(a-2)
